Math 513,  Au 2008

Office hours: Monday and Friday, 11:00 a.m.- noon, and by appointment.
Tutoring offered at MSLC, Tuesdays 1-3 p.m.

Homework up to Oct 22

F Oct. 24
Topics:
3.2
Homework:
Write up the solutions and turn in for grading on Monday Oct. 27: 3.2: 1,2,3,4 (Note: this homework set is worth a maximum of 2 points.)

M Oct. 27
Topics:
3.3
HW: Write up the solutions and turn in for grading on M Nov 3rd: 3.3: 2, 3, 4, 5, 6, 8, 10

W Oct. 29
Topics:
HW: Write up the solutions and turn in for grading on M Nov 3rd: 3.4: 2, 4, 6, 7, 9, 12

F Oct. 31
Topics:
3.5, From 3.7:Taylor series, the Hessian - see Examples 3.23, 3.24, 3.25. (No diadics.)
HW: Write up the solutions and turn in for grading on M Nov 3rd: 3.5: 4, 5, 6, 7, 8, 3.7: 2, 3

M Nov. 3rd
Topics:
3.7 continued: the second derivative test (using the eigenvalues of the Hessian matrix).
Web resources: Multiplying matrices and vectors, Taylor's polynomials, Local extrema (pictures), Hessian matrix and the second derivative test
HW: Write up the solutions and turn in for grading on M Nov 10: 3.6: the two problems below:
A. Find the critical points of the scalar field f(x,y,z)=(x+y-z)^2+y^2+z^2 and use the eigenvalues of the Hessian matrix to decide if these points are max, min, saddle.
B. Same questions for f(x,y,z)=x^2+y^2-z^2.

W Nov. 5
Topics:
3.6
HW: Write up the solutions and turn in for grading on M Nov 10: 3.6: 1, 2, 4, 5, 7, 8 Note: the Laplacian of a vector field is calculated by taking the Laplacian of each component (see the example on p.139 up).

F Nov. 7
Topics:
4.1
HW: Write up the solutions and turn in for grading on M Nov 10: 4.1: 2, 3, 4, 5, 11, 12, 14, 19, 20

Note: If you would like to have more time, you can turn in the homework on W Nov 12 (instead of M Nov 10).

M Nov. 10
Topics:
4.2
HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): For each of the following regions ( sketch them and) state and justify: 1) is it open? 2) is it closed? 3) What is its boundary? 4) Is is a domain? (Note: <= stands for "less or equal".)

A. 1<x^2+y^2<4 ; B. 1<=x^2+y^2<=4 ; C. 1<x^2+y^2<=4 ; D. 0<x^2+y^2<4 ; E. |x|>=1 in the plane ; F. |x|>1 in space

W Nov. 12
Topics:
4.2, start 4.3
HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): 4.2: 2 (see formula (D1) p 353), 4, 6, 7;

F Nov. 14
Topics:
4.3
HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): 4.3:1, 2a) c) e), 3a) c) e), 6, 7; Note: disregard a),c),e) in 3 (it is a typo).

M Nov. 17
Topics:
4.4
HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): 4.4: 1a) c) e), 2, 4, 5, 6, 7

Special office hours: this W 11-12.

Extra practice problems: 4.4: 9b, 10. Read the text and work out the examples 4.7 (page 208), 4.8

W Nov. 19
Review.
See a Review guide for midterm 2. Note: midterm 2 covers problems similar to those in sections from 3.1 to 4.4. However, we need to use previous knowledge!

F Nov. 21 Midterm 2

M Nov. 24
Topics:
Start 4.6
HW: Brush up calculation of double integrals using ; choose the path 3.Calculus Book III > 5.Integration > 2.Double Integrals > Double integrals I

W Nov. 26
Topics:
4.6, 4.7
HW: Write up the solutions and turn in for grading on M: 4.6: 2, 4, 5, 6, 4.7: 2 a) c) g), 3, 5, 8, 11, 13, 15 Also: Review the calculation of triple integrals (you may use the link to COW).

M Dec 1
Topics:
4.8
HW: 4.8: 1, 3, 4 a) b), 6

W Dec 3 and F Dec 5
Topics:
4.9
HW: 4.9: 1, 2, 3 b), 4, 8, 9, 12, 15, 17, 20.

Final examination info: You are allowed to bring and use one page (front and back) with your own notes. Here is a Review Guide. Please check the

I will be available on Friday Dec. 12, from 11 a.m. to noon if you want to see your graded final exam. However, I hope to have everything ready by Thursday, and if so, I will post here a time when I will be in my office on Thursday too.

Gibbs's lectures on Vector Calculus